Fuzzy cognitive maps (FCMs) have been widely used in time series prediction due to the excellent performance in dynamic system modeling. However, existing time series prediction methods based on FCMs have some defects, such as low precision and sensitivity to hyper parameters. Therefore, more accurate and robust methods remain to be proposed for handling non-stationary and large-scale time series. To address this issue, in this paper, a novel time series prediction method based on empirical mode decomposition (EMD) and high-order FCMs (HFCMs) is proposed, termed as EMD-HFCM. First, EMD is applied to extract features from the original sequence to obtain multiple sequences to represent the nodes of HFCM. To learn HFCM efficiently and accurately, a robust learning method based on Bayesian ridge regression is employed, which can estimate the regular parameters from data instead of being set manually. Then, prediction can be performed based on the iterative characteristics of HFCM. To compare EMD-HFCM with existing methods, extensive experiments are conducted on eight benchmark datasets and the results validate the performance of the proposal in handling large-scale and non-stationary time series. Furthermore, the experiments also show that the proposed method is much more robust and insensitive to hyper parameters than the state of art methods. Finally, non-parametric statistical tests are carried out and the superiority of the proposed method is verified in the statistical sense.

由于动态系统建模的出色性能，模糊认知图（FCM）已广泛用于时间序列预测。然而，现有的基于FCM的时间序列预测方法存在一些缺陷，例如精度低和对超参数的敏感性。因此，仍有待提出更准确和鲁棒的方法来处理非平稳和大规模的时间序列。针对这一问题，本文提出了一种基于经验模态分解（EMD）和高阶FCM（HFCM）的时间序列预测方法，称为EMD-HFCM。首先，将EMD应用于从原始序列中提取特征，以获得代表HFCM节点的多个序列。为了有效，准确地学习HFCM，我们采用了一种基于贝叶斯岭回归的鲁棒学习方法，可以从数据中估算常规参数，而无需手动设置。然后，可以基于HFCM的迭代特性执行预测。为了将EMD-HFCM与现有方法进行比较，对八个基准数据集进行了广泛的实验，结果验证了该建议在处理大规模和非平稳时间序列中的性能。此外，实验还表明，与现有方法相比，该方法对超参数的鲁棒性和敏感性更高。最后，进行了非参数统计检验，并从统计意义上验证了该方法的优越性。在八个基准数据集上进行了广泛的实验，结果验证了该建议在处理大规模和非平稳时间序列方面的性能。此外，实验还表明，与现有方法相比，该方法对超参数的鲁棒性和不敏感性更高。最后，进行了非参数统计检验，并从统计意义上验证了该方法的优越性。在八个基准数据集上进行了广泛的实验，结果验证了该建议在处理大规模和非平稳时间序列方面的性能。此外，实验还表明，与现有方法相比，该方法对超参数的鲁棒性和敏感性更高。最后，进行了非参数统计检验，并从统计意义上验证了该方法的优越性。